Donald Trump backed away from further military confrontation with Iran on Wednesday after days of escalating tensions, saying Tehran appeared to be standing down following missile attacks on two Iraqi bases hosting US and coalition troops.

Flanked by the vice-president, Mike Pence, the defense secretary, Mark Esper, and other high ranking military officials in uniform, Trump delivered remarks in the Grand Foyer of the White House, hours after Iran declared the attack to be retaliation for the US drone strike last week that killed the senior Iranian Gen Qassem Suleimani.

“Iran appears to be standing down, which is a good thing for all parties concerned and a very good thing for the world,” Trump said, reading from teleprompters. “No American or Iraqi lives were lost because of the precautions taken, the dispersal of forces, and an early warning system that worked very well.”

Later, the chairman of the joint chiefs of staff, General Mark Milley, said the nature of the missile damage at the targeted bases suggested the attack was intended to take US and allied lives.

“I believe, based on what I saw and what I know, that they were intended to cause structural damage, destroy vehicles and equipment and aircraft and to kill personnel. That’s my own personal assessment,” Milley said. Satellite images showed the missiles destroyed buildings at al-Asad base in Anbar province.

A few hours after the president spoke, the fortified diplomatic area in Baghdad, the Green Zone, was hit by two rockets. Initial reports suggest they were fired locally, and caused no casualties, but they were a reminder of the threat of Iraqi militias, some with close ties to Tehran.

Trump’s speech was notably more sober than his more bellicose statements and tweets in the immediate aftermath of Suleimani’s killing, in which he threatened to bomb Iranian cultural sites, a potential war crime. The United States, in recent days, deployed 3,500 paratroopers to the Middle East and Americans were urged to leave the region over safety concerns.

Trump said the United States would continue evaluating options “in response to Iranian aggression” and that additional sanctions on the Iranian regime would be imposed. He did not elaborate. Iran is already so heavily sanctioned that few experts believe that further US measures would make much economic difference.

The president stressed the considerable power of the United States military but said that his administration did not seek conflict.

“Our missiles are big, powerful accurate lethal and fast. Under construction are many hypersonic missiles,” Trump said. “The fact that we have this great military and equipment, however, it does not mean we have to use it. We do not want to use it.”

The president, who is campaigning for re-election in November, has faced fierce criticism from senior Democrats in recent days over his administration’s handling of the standoff. Joe Biden, the former vice-president seen as the frontrunner for the presidential nomination, accused Trump brought the United States “dangerously close” to war with Iran.

Senior administration officials briefed Congress behind closed doors on the decision to target Suleimani and other aspects of the crisis, but they were castigated on both sides of the aisle for being evasive on major issues.

“There were so many important questions that they did not answer,” said Democratic senator Chuck Schumer. “As the questions began to get tough, they walked out.”

Republican senator Mike Lee called it “the worst briefing I’ve had on a military issue in my nine years” in the Senate, according to CNN. Lee called the administration’s handling of the crisis “un-American” and “completely unacceptable”.

On Thursday, the House of Representatives will vote on a war powers resolution that demands an end to US military action against Iran without congressional approval.

Trump’s address came after Iran launched more than a dozen missiles at Iraqi bases hosting US and coalition troops. Al-Asad airbase in Iraq’s Anbar province was hit 17 times, including by two ballistic missiles that failed to detonate, according to the Iraqi government. A further five missiles were targeted at a base in the northern city of Erbil in the assault, which began at about 1.30am local time on Wednesday.

The Iranian foreign minister, Javad Zarif, made clear the strikes had “concluded” early on Wednesday morning, and characterised them as “proportionate measures in self-defence” rather than an act of war.

“We do not seek escalation or war, but will defend ourselves against any aggression,” Zarif wrote on Twitter.

However, while both sides appeared to step back from confrontation in the short term, analysts have warned that the standoff may continue to play out through proxies in the Middle East. Security experts have also warned of possible Iranian cyber attacks on critical infrastructure.

Iran’s supreme leader, Ali Khamenei, described the bombings as “a slap in the face” for the US but warned Tehran still had a wider goal of expelling its enemy from the region. The Iranian president, Hassan Rouhani, said the “final answer” to the assassination would be to “kick all US forces out of the region”.

In his Wednesday address, Trump again vowed that he would not allow Iran to obtain a nuclear weapon and urged world powers to quit a 2015 nuclear accord with Iran that Washington abandoned in 2018 and work for a new deal, an issue that has been at the heart of rising tensions between Washington and Tehran. Iran has denied it seeks nuclear weapons, and rejected new talks.

“The time has come for the United Kingdom, Germany, France, Russia and China to recognize this reality,” Trump said. “They must now break away from the remnants of the Iran deal or JCPOA. And we must all work together toward making a deal with Iran, that makes the world a safer and more peaceful place.”

Trump also said he would ask Nato to “become much more involved in the Middle East process”, without elaborating. Trump in the past has repeatedly criticized the alliance and further alienated his European partners by failing to warn them about the Suleimani killing.

There was no immediate reaction from Iranian officials to Trump’s comments. The semi-official Fars news agency described the US president’s remarks as a “big retreat from threats”.

Ned Price, a former CIA official who also worked on the National Security Council during Barack Obama’s administration, said that the speech had moved the United States somewhat away from the brink of war with Iran.

“President Trump’s reckless approach has created a dangerous reality in which the best case scenario would be avoiding war with Iran,” Price said. “With his address today, Trump may have met that exceedingly low bar, but just barely. At the same time, his actions are not consequence-free. Far from it, as Americans around the world and our partners are now under increased threat from an array of challenges.”

But Price also noted that by authorizing the Suleimani killing, Trump had “galvanized Tehran’s proxy and military forces into action”.

“If history is any guide, they will seek to take on a months’ or even years’-long effort to seek vengeance for Suleimani’s death, taking advantage of their presence throughout the region and even beyond,” Price added.

Additional reporting: Michael Safi in Beirut, Oliver Holmes and Ghaith Abdul-Ahad in Baghdad